The importance of shields against neutron-induced background in new classes of gamma-ray detectors such as CZT has been emphasized for various reasons, for example: large cross sections for neutron interactions in detector materials and inefficiency of vetoing those events by conventional active shields. We demonstrated through Monte Carlo simulations how our new approach, supershields, which consist of 3 different layers, are superior to the monolithic neutron shields which have been developed in the past. We verify the performance of these supershields through lab experiments using mono-energetic low-energy neutron beams at RARAF and compare with the case of monolithic neutron shields. The results of lab experiments along with Monte Carlo simulations will be the guide to optimal designs of supershields for existing and next-generation gamma-ray experiments and subsequently to improving performance of those experiments.